Shock Standoff Research Articles

Experiment on similarity between wake flow field and electromagnetic scattering characteristic of the hypersonic model

The plasma sheath and wake flow of the hypersonic vehicle can affect the electromagnetic scattering characteristics of the reentry targets when they pass through the earth atmosphere at high speed. In order to study the similarity between the wake and the characteristic of the model launched at high velocity, the simulation experiments on the electromagnetic scattering characteristics of the spherical models made of Al2O3 and their wakes are carried out under the same binary scaling parameters in the ballistic range. The models are launched by the two-stage light-gas gun. The diameters of the models are 8 mm, 10 mm, 12 mm and 15 mm, respectively, while the pressures of the target chamber are 6.3 kPa, 5.0 kPa, 4.2 kPa and 3.3 kPa, respectively. The shock standoff distance is obtained by the shadow graph system. The electron density distribution of the wake is measured by the electron density measurement system. The RCS distribution of the wake and the model are acquired by X band monostatic radars, whose visual angle is 40. The results show that the shock standoff distance gradually increases with the increasing of the model dimension under the conditions of the same velocity and binary scaling parameters. The wake electron densities of different models are similar in their variation trends and orders of magnitude. The wake flow field of the different models with high velocity are the same as the results predicted by the double scale laws. The RCS distributions and total RCS of the wake of the models are different from each other. The electromagnetic scattering properties of the wake flow field of the various models do not conform with the predicted results obtained from the double scale law. The electromagnetic scattering energy is distributed over the regions of the models made up of aluminium oxide and the wake zones. There appears to be one center of the electromagnetic scattering energy in the area of the model coated with flow field, while several centers emerge in the region of the wake. The measuring signals of the RCS of the models show a random distribution, because the amplitude variation of the RCS and the frequency change of the RCS are random. The total RCS of the model increases with the increase of the model dimension, but the variation range of ripple frequency decreases with the increase of the model dimension.

COMPRESSIBLE FLOW IN FRONT OF AN AXISYMMETRIC BLUNT OBJECT: ANALYTIC APPROXIMATION AND ASTROPHYSICAL IMPLICATIONS

ABSTRACT Compressible flows around blunt objects have diverse applications, but current analytic treatments are inaccurate and limited to narrow parameter regimes. We show that the gas-dynamic flow in front of an axisymmetric blunt body is accurately derived analytically using a low order expansion of the perpendicular gradients in terms of the parallel velocity. This reproduces both subsonic and supersonic flows measured and simulated for a sphere, including the transonic regime and the bow shock properties. Some astrophysical implications are outlined, in particular for planets in the solar wind and for clumps and bubbles in the intergalactic medium. The bow shock standoff distance normalized by the obstacle curvature is in the strong shock limit, where g is the compression ratio. For a subsonic Mach number M approaching unity, the thickness δ of an initially weak, draped magnetic layer is a few times larger than in the incompressible limit, with amplification .

Coronal magnetic field profiles from shock‐CME standoff distances

AbstractCoronagraphs observe coronal mass ejections (CMEs) and driven shocks in white light images. From these observations the shock's speed and the shock's standoff distance from the CME's leading edge can be derived. Using these quantities, theoretical relationships between the shock's Alfvénic Mach number MA and standoff distance, and empirical radial profiles for the solar wind velocity and number density, the radial magnetic field profile upstream of the shock can be calculated. These profiles cannot be measured directly. We test the accuracy of this method for estimating the radial magnetic field profile upstream of the shock by simulating a sample CME that occurred on 29 November 2013 using the three‐dimensional (3‐D) magnetohydrodynamic Block‐Adaptive‐Tree‐Solarwind‐Roe‐Upwind‐Scheme code, retrieving shock‐CME standoff distances from the simulation, and comparing the estimated and simulated radial magnetic field profiles. We find good agreement between the two profiles (within ±30%) between 1.8 and 10 R⊙. Our simulations confirm that a linear relationship exists between the standoff distance and the inverse compression ratio at the shock. We also find very good agreement between the empirical and simulated radial profiles of the number density and speed of the solar wind and inner corona.

Effect of nose shape on the shock standoff distance at nearsonic flows

This paper describes a numerical solution of the bow shock shape ahead of some blunt and sharp axisymmetric noses containing sphere, blunt cone, and sharp cone at steady transonic flow in the Mach number range of 1.01 to 1.2. For validating the results, one sphere and three blunt cones are modeled, and their shock standoff distance is compared with other experimental and numerical studies. The flow over other noses with similar geometric parameters is then solved and compared with each other. In this study, the Reynolds-averaged Navier—Stokes equations are solved using the Spalart—Allmaras turbulence model. The purpose of this study is to determine the shock standoff distance for some blunt and sharp noses at low supersonic free flight speed. The shock standoff distance is determined from the Mach number curve on the symmetry line. The present numerical simulations reach down to M8=1.01 a range where it is almost very difficult to set in experimental studies. The shock wave locations were found to agree well with previous numerical and experimental studies. Our results are closer to the experimental results compared to other numerical studies. In addition, the results for shock standoff distances over paraboloids in these speed ranges have not been previously published as far as we know.

Flow Field Analysis on the Stagnation Streamline of a Blunt Body

The hypersonic flow on the stagnation streamline of a blunt body is analyzed with quasi one-dimensional (1-D) Navier-Stokes equations approximated by adopting the local similarity to the two-dimensional (2-D)/axisymmetric Navier-Stokes equations. The governing equations are solved using the implicit finite volume method. The computational domain is confined from the stagnation point to the shock wave, and the shock fitting method is used to find the shock position. We propose a boundary condition at the shock, which employs the shock wave angle in the vicinity of the stagnation streamline using the shock shape correlation. As a result of numerical computation conducted for the hypersonic flow over a sphere, the proposed boundary condition is shown to improve the accuracy of the prediction of the shock standoff distance. The quasi 1-D Navier-Stokes code is efficient in computing time and is reliable for the flow analysis along the stagnation streamline and the prediction of heat flux at the stagnation point in the hypersonic blunt body flow.

Impingement Tones and Associated Shock Instabilities in Supersonic Plug Nozzle Flows

An investigation into a supersonic impinging jet emitted from a truncated plug nozzle is presented for a nozzle pressure ratio of 3.4. High-resolution schlieren and acoustic measurements verify that the jet behavior close to the nozzle is significantly different from round jets. Impingement tones are not observed for plate distances less than 3.2 nozzle diameters from the throat. Sufficiently far downstream from the nozzle, the jet shock structure is similar to that of a round jet. Ultrahigh-speed schlieren is used to track the motion of the standoff shock located above the impingement plate. The shock-oscillation frequency matches the impingement-tone frequency within statistical uncertainty. The average shock standoff distance and oscillation amplitude are related to the relative position of the impingement plate with respect to the shock structure in the equivalent freejet. Shock splitting is directly observed for certain plate distances.

Delusive Influence of Nondimensional Numbers in Canonical Hypersonic Nonequilibrium Flows

AbstractA finite volume–based unstructured inviscid flow solver has been developed for the study of nonequilibrium effects in high enthalpy flows. Four different inviscid flux computation schemes are tested for literature reported test cases like unsteady wave motion in a shock tube and high enthalpy flow over cylinder/sphere. During the present assessment, encouraging agreement has been noticed in capturing all the essential flow features in the reacting media. Here, the Rusanov scheme is noticed to be computationally cheaper among all the schemes with noticeable diffusion around strong gradients. Shock tube test case revealed the existence of various shock Mach numbers for a given driving pressure ratio in the presence of reactions. Similarly, freestream Mach number is found to have limitations in representing the shock standoff distance in case of high enthalpy flow over cylinder and sphere. In line with this, real gas effects are prominently observed for the case of the cylinder in comparison with the...

Numerical investigation on the thermal protection mechanism for blunt body with forward-facing cavity

Numerical experiments are carried out using the standard hypersonic ballistic-type model (HB-2) to investigate the effect of forward-facing cavity on the aerodynamic heating. A general concept is proposed which utilizes the flow disturbances generated passively in the nosed subsonic region to weaken the detached shock wave. Several aspects are mainly studied, including shock shape and standoff distance, surface heat flux and pressure, flowfield feature and cooling mechanism. The numerical results indicate that shock strength and standoff distance increase with an increase in the L/D ratio of the cavity. Interestingly, a bulge structure of the detached shock associated with a deep cavity is observed for the first time. Local surface heat flux and pressure around the concave nose are much lower respectively than those at the stagnation point of the baseline model. In addition, both surface heat and pressure reductions are proportional to the L/D ratio. A negative heating phenomenon may occur in the vicinity of a sharp lip or on the base wall of a deep cavity. If the L/D ratio exceeds 0.7, the detached shock appears as a self-sustained oscillation which can be referred to as the cooling mechanism.

Численное моделирование МГД управления сверхзвуковым потоком в среде OpenFOAM

MHD flow control is a relevant topic in today’s aerospace engineering. An OpenFOAM density-based solver that is capable of handling MHD supersonic flow problems with constant magnetic field is developed. The proposed solver is based on Balbas-Tadmor central difference schemes. This solver can be applied to studying the potential of MHD flow control systems for atmospheric entry vehicles. A supersonic flow around a spherically blunt cone both with and without MHD interaction is studied. Gases with thermodynamic parameters characteristic for Earth’s and Martian atmospheres are considered. The results show visible effect of magnetic field on surface temperature of the body. The differences between shock standoff distances and general shockwave configurations of MHD and non-MHD flow are also apparent. The solution is stable for Stuart number below 0.2. Conditional instability of the solver can be attributed to the MHD term’s contribution to the local speed of sound and can be avoided by taking it into account. The developed application has proven the suitability of the used schemes for resolving steep gradients in MHD supersonic flow problems. The study itself has shown theoretical possibility of studying the MHD flow control using OpenFOAM. Further research may include an effort to stabilize the solver and to enhance the mathematical model of the flow.

Survey of shock-wave structures of smooth-particle granular flows.

We show the effects of simulated supersonic granular flow made up of smooth particles passing over two prototypical bodies: a wedge and a disk. We describe a way of computationally identifying shock wave locations in granular flows and tabulate the shock wave locations for flow over wedges and disks. We quantify the shock structure in terms of oblique shock angle for wedge impediments and shock standoff distance for disk impediments. We vary granular flow parameters including upstream volume fraction, average upstream velocity, granular temperature, and the collision coefficient of restitution. Both wedges and disks have been used in the aerospace community as prototypical impediments to flowing air in order to investigate the fundamentally different shock structures emanating from sharp and blunt bodies, and we present these results in order to increase the understanding of the fundamental behavior of supersonic granular flow.

An Application of the Stereoscopic Self-similar-Expansion Model to the Determination of CME-Driven Shock Parameters

We present an application of the stereoscopic self-similar-expansion model (SSSEM) to Solar Terrestrial Relations Observatory (STEREO)/Sun-Earth Connection Coronal and Heliospheric Investigation (SECCHI) observations of the 03 April 2010 CME and its associated shock. The aim is to verify whether CME-driven shock parameters can be inferred from the analysis of j-maps. For this purpose we use the SSSEM to derive the CME and the shock kinematics. Arrival times and speeds, inferred assuming either propagation at constant speed or with uniform deceleration, show good agreement with Advanced Composition Explorer (ACE) measurements. The shock standoff distance $[\Delta]$, the density compression $[\frac{\rho_d}{\rho_u}]$ and the Mach number $[M]$ are calculated combining the results obtained for the CME and shock kinematics with models for the shock location. Their values are extrapolated to $\textrm{L}_1$ and compared to in-situ data. The in-situ standoff distance is obtained from ACE solar-wind measurements, and the Mach number and compression ratio are provided by the Harvard-Smithsonian Center for Astrophysics interplanetary shock database. They are $\frac{\rho_d}{\rho_u} =2.84$ and $M = 2.2$. The best fit to observations is obtained when the SSSEM half width $\lambda = 40 \deg$ and the CME and shock propagate with uniform deceleration. In this case we find $\Delta = 23 \textrm{R}_{\odot}$, $\frac{\rho_d}{\rho_u} =2.61$, and $M = 2.93$. The study shows that CME-driven shock parameters can be estimated from the analysis of time-elongation plots and can be used to predict their in-situ values.

THE PLASMA ENVIRONMENT IN COMETS OVER A WIDE RANGE OF HELIOCENTRIC DISTANCES: APPLICATION TO COMET C/2006 P1 (MCNAUGHT)

On 2007 January 12, comet C/2006 P1 (McNaught) passed its perihelion at 0.17 AU. Abundant remote observations offer plenty of information on the neutral composition and neutral velocities within 1 million kilometers of the comet nucleus. In early February, the Ulysses spacecraft made an in situ measurement of the ion composition, plasma velocity, and magnetic field when passing through the distant ion tail and the ambient solar wind. The measurement by Ulysses was made when the comet was at around 0.8 AU. With the constraints provided by remote and in situ observations, we simulated the plasma environment of Comet C/2006 P1 (McNaught) using a multi-species comet MHD model over a wide range of heliocentric distances from 0.17 to 1.75 AU. The solar wind interaction of the comet at various locations is characterized and typical subsolar standoff distances of the bow shock and contact surface are presented and compared to analytic solutions. We find the variation in the bow shock standoff distances at different heliocentric distances is smaller than the contact surface. In addition, we modified the multi-species model for the case when the comet was at 0.7 AU and achieved comparable water group ion abundances, proton densities, plasma velocities, and plasma temperatures to the Ulysses/SWICS and SWOOPS observations. We discuss the dominating chemical reactions throughout the comet-solar wind interaction region and demonstrate the link between the ion composition near the comet and in the distant tail as measured by Ulysses.

A survey of solar wind conditions at 5 AU: a tool for interpreting solar wind-magnetosphere interactions at Jupiter

We examine Ulysses solar wind and interplanetary magnetic field (IMF) observations at 5 AU for two ~13 month intervals during the rising and declining phases of solar cycle 23 and the predicted response of the Jovian magnetosphere during these times. The declining phase solar wind, composed primarily of corotating interaction regions and high-speed streams, was, on average, faster, hotter, less dense, and more Alfvenic relative to the rising phase solar wind, composed mainly of slow wind and interplanetary coronal mass ejections. Interestingly, none of solar wind and IMF distributions reported here were bimodal, a feature used to explain the bimodal distribution of bow shock and magnetopause standoff distances observed at Jupiter. Instead, many of these distributions had extended, non-Gaussian tails that resulted in large standard deviations and much larger mean over median values. The distribution of predicted Jupiter bow shock and magnetopause standoff distances during these intervals were also not bimodal, the mean/median values being larger during the declining phase by ~1 – 4%. These results provide data-derived solar wind and IMF boundary conditions at 5 AU for models aimed at studying solar wind-magnetosphere interactions at Jupiter and can support the science investigations of upcoming Jupiter system missions. Here, we provide expectations for Juno, which is scheduled to arrive at Jupiter in July 2016. Accounting for the long-term decline in solar wind dynamic pressure reported by McComas et al. (2013), Jupiter’s bow shock and magnetopause is expected to be at least 8 – 12% further from Jupiter, if these trends continue.

Active current sheets and candidate hot flow anomalies upstream of Mercury's bow shock

Hot flow anomalies (HFAs) represent a subset of solar wind discontinuities interacting with collisionless bow shocks. They are typically formed when the normal component of the motional (convective) electric field points toward the embedded current sheet on at least one of its sides. The core region of an HFA contains hot and highly deflected ion flows and rather low and turbulent magnetic field. In this paper, we report observations of possible HFA‐like events at Mercury identified over a course of two planetary years. Using data from the orbital phase of the MESSENGER mission, we identify a representative ensemble of active current sheets magnetically connected to Mercury's bow shock. We show that some of these events exhibit magnetic and particle signatures of HFAs similar to those observed at other planets, and present their key physical characteristics. Our analysis suggests that Mercury's bow shock does not only mediate the flow of supersonic solar wind plasma but also provides conditions for local particle acceleration and heating as predicted by previous numerical simulations. Together with earlier observations of HFA activity at Earth, Venus, Mars, and Saturn, our results confirm that hot flow anomalies could be a common property of planetary bow shocks and show that the characteristic size of these events is controlled by the bow shock standoff distance and/or local solar wind conditions.

On the shape and motion of the Earth's bow shock

Multipoint-measurements by the magnetic field Cluster-FGM (Flux Gate Magnetometer) are used to determine the local shock normal, and in turn allow the study of shock location shape and the velocity of the Earth's bow shock. The shock crossings cover orbits in which the spacecraft separation is of the order of ~600km or less. A data selection of 133 bow shock crossings, ranging from quasi-steady perpendicular to moderately noisy oblique geometries, have been analyzed using a standard timing analysis. Prior to applying the timing technique, the magnetic field fluctuations, when present, are suppressed using low band-pass filtering. The present study contributes to similar studies conducted in the past and available in the literature through the inclusion of a larger data set. The shock standoff distance is determined conjointly with a paraboloid model and the results from a timing analysis. A statistical study reveals a standoff distance well in agreement with the standard gas dynamics model prediction for high Mach number MA. We have also found that for about half the crossings, the timing shock normals agree, within 11°, with a conic-based shock model. Our results strongly indicate that the motion of the shock is predominantly along the Sun–Earth direction; a departure from this direction is not related to the shock-crossing location. Shock velocities below ~80km/s satisfactorily follow a nearly Gaussian distribution with zero mean and a standard deviation of ~42km/s. Finally, we show that high speed motions are correlated with sharp increases in the solar wind upstream ram pressure, and are consistent with gas dynamics model predictions.

Hypersonic Flow over a Cylinder with a Nanosecond Pulse Electrical Discharge

A computational study of Mach 5 airflow over a cylinder with a dielectric barrier discharge actuator was performed. The actuator was pulsed at nanosecond time scales and it rapidly added thermal energy to the flow, creating a shock wave that traveled away from the pulse source. As the shock wave traveled upstream, it interacted with the standing bow shock, and temporarily increased the bow shock standoff distance. This phenomenon was also observed experimentally through phase-locked schlieren photography. This paper aims to reproduce flow phenomena observed in the experiment using high-fidelity computations in order to provide additional insight into the shock–shock interaction, and subsequent effect on the cylinder, through a reduced-order phenomenological model of the actuator. A three-dimensional simulation of the experiment was able to accurately capture the complex cylinder/tunnel-sidewall interaction, and to replicate the changes in the flow produced by the nanosecond dielectric barrier discharge. The results show that the device was very effective at moving the standing bow shock for a minimal energy budget.

Hypervelocity shock standoff on spheres in air

To provide data for the validation of computational fluid dynamics models, measurements of the shock standoff distance on spheres in hypervelocity flows have been made. Test flows of air at 8.7 and 9.7 km/s were generated in the X2 expansion tunnel fitted with a Mach 10 nozzle. High-speed video images were analysed with a least-squares shape-fitting algorithm. Assuming a spherical shock shape near the nose enabled increased resolution measurements beyond the native pixel size. Normalised shock standoff distances, \(\Delta \)/\(D\), in the range 0.03–0.04 were measured, with sphere diameters, \(D\), of 40, 60 and 80 mm.

Gravity-driven granular free-surface flow around a circular cylinder

AbstractSnow avalanches and other hazardous geophysical granular flows, such as debris flows, lahars and pyroclastic flows, often impact on obstacles as they flow down a slope, generating rapid changes in the flow height and velocity in their vicinity. It is important to understand how a granular material flows around such obstacles to improve the design of deflecting and catching dams, and to correctly interpret field observations. In this paper small-scale experiments and numerical simulations are used to investigate the supercritical gravity-driven free-surface flow of a granular avalanche around a circular cylinder. Our experiments show that a very sharp bow shock wave and a stagnation point are generated in front of the cylinder. The shock standoff distance is accurately reproduced by shock-capturing numerical simulations and is approximately equal to the reciprocal of the Froude number, consistent with previous approximate results for shallow-water flows. As the grains move around the cylinder the flow expands and the pressure gradients rapidly accelerate the particles up to supercritical speeds again. The internal pressure is not strong enough to immediately push the grains into the space behind the cylinder and instead a grain-free region, or granular vacuum, forms on the lee side. For moderate upstream Froude numbers and slope inclinations, the granular vacuum closes up rapidly to form a triangular region, but on steeper slopes both experiments and numerical simulations show that the pinch-off distance moves far downstream.

Thermochemical nonequilibrium modeling of a low-power argon arcjet wind tunnel

Non-transferred low-power arcjet wind tunnels with pure argon working gas are widely used as inexpensive laboratory plasma sources to simulate a weakly ionized supersonic flow around an atmospheric entry vehicle. Many experiments using argon arcjet wind tunnels have been conducted, but their numerical modeling is not yet complete. We develop an axisymmetric Navier-Stokes model with thermochemical nonequilibrium and arc discharge that simulates the entire flow field in a steady-operating argon arcjet wind tunnel, which consists of the inside of the arcjet and its arc plume entering a rarefied vacuum chamber. The computational method we develop makes it possible to reproduce the arc column behavior far from thermochemical equilibrium in the low-voltage discharge mode typical of argon arcjets. Furthermore, the results reveal that the plasma characteristic of being far from thermal equilibrium, which is particular to argon, causes the arcjet to operate in the low-voltage mode and its arc plume to be completely thermochemically frozen. Moreover, the arc plume has electroconductive non-uniformity with an electrically insulating boundary in the radial direction. Our computed values for the shock standoff distance in front of a blunt body and the drag exerted on it agree with measured values. As a result, the self-consistent computational model in this study is useful in investigating thermochemical nonequilibrium plasma flows in argon arcjet wind tunnels.

Heat release effects on drag reduction in high speed flows

Heat addition due to exothermic reactions of ablated chromium in hypersonic flow on coated blunt bodies is numerically investigated. The advection upstream splitting method is used as computational scheme. Conjugate heat transfer is considered by simultaneous solution of flow and solid phase governing equations to compute the surface regression rate. The results show that using such coatings on blunt noses in high speed flows will increase the shock standoff distance and decrease the aerodynamic drag but not so much that previously reported. Using these simulations, the chromium proper thickness will be estimated more precisely for specific flight mission.